The unit of percentage error is

The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)

Durring Searle's experiment, zero of the Vernier scale lies between $3.20 \times 10^{-2} m$ and $3.25 \times 10^{-2} m$ of the main scale. The $20^{\text {th }}$ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of $2 \ kg$ is applied to the wire, the zero of the Vernier scale still lies between $3.20 \times 10^{-2} m$ and $3.25 \times 10^{-2} m$ of the main scale but now the $45^{\text {th }}$ division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is $2 m$. and its cross-sectional area is $8 \times 10^{-7} m ^2$. The least count of the Vernier scale is $1.0 \times 10^{-5} m$. The maximum percentage error in the Young's modulus of the wire is

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

If a copper wire is stretched to make its radius decrease by $0.1\%$ , then percentage increase in resistance is approximately .......... $\%$

A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?

$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds

$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second

$(C)$ Percentage error in the determination of $g$ is $5 \%$

$(D)$ Percentage error in the determination of $g$ is $2.5 \%$